Mathematical Analysis – Linear Algebra

Professors Michael Filippakis
Course category Core
Course ID DS-006
Credits 7
Lecture hours 4 hours
Lab hours 3 hours
Digital resources View on Aristarchus (Open e-Class)

Learning Outcomes

The course’s material includes mathematical definitions, results and reasoning methodologies that pertain to basic mathematical analysis and linear algebra objects and models underlying the foundations and applications of computer science. Moreover the relevant connections of mathematical analysis and linear algebra to several more specific branches of computer science are presented. The course directly supports most of the curriculum subjects and courses. Note that during the course specific examples of application are discussed using new technologies with the help of programs such as Matlab, and Octave.

Upon successfully completion of the course the students will be in position to:·

  • Know and understand basic analysis method of mathematical analysis and linear algebra (indicatively: sequences, series, functions of one variable (differentiation, integration), differential equations, matrices, determinants, linear systems, inner product, characteristics values, orthogonal diagonalization)·
  • Choose the appropriate mathematical concepts and representations for each problem at hand. In addition to develop mathematical thinking and be able to analyze and adapt acquired knowledge to applications of computer science·
  • Combine the basic components of calculus and algebra to solve more complex mathematical problems.·
  • Know, handle and understand Matlab and Octave programs on applications of mathematical analysis and linear algebra to computer science.

Course Contents

  • Sequences. Series.
  • Functions of One Variable.
  • Differentiation.
  • Iterative Methods for Solving Equations.
  • Polynomial Approximation of Functions.
  • Numerical Differentiation.
  • Indefinite Integral. Differential Equations.
  • Definite Integral.
  • Algebraic Structures: Groups. Rings.
  • Fields. Vector Spaces.
  • Basic Linear Algebra: Matrices. Determinants. Linear Systems.
  • Characteristics of a Matrix: Eigenvalues. Eigenvectors. Diagonalization of Matrices. Bilinear Forms.
  • Inner Product: Orthonormalization. Gram-Schmidt Algorithm.
  • Linear Transformation Matrices: Change of bases matrix. Matrix of a linear transformation.

Recommended Readings

  • M.Filippakis, Applied Analysis and Linear Algebra, Tsotras Publications, Athens 2017, 2nd Edition.
  • Χ. Moisiadis, Advanced Mathematics.
  • Teaching Notes.